Pith Number

pith:N3DOP3WM

pith:2015:N3DOP3WMQ4AVB57DNG4R5HVV7I

not attested not anchored not stored refs pending

On $P$-adic Ising-Vannimenus model on an arbitrary order Cayley tree

Farrukh Mukhamedov, Mansoor Saburov, Otabek Khakimov

arxiv:1510.03129 v1 · 2015-10-12 · math.DS · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N3DOP3WMQ4AVB57DNG4R5HVV7I}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:29:40.233195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ec6e7eecc870150f7e369b91e9eb5fa3ba983aa26607206f4ec64f52809eb77

Aliases

arxiv: 1510.03129 · arxiv_version: 1510.03129v1 · doi: 10.48550/arxiv.1510.03129 · pith_short_12: N3DOP3WMQ4AV · pith_short_16: N3DOP3WMQ4AVB57D · pith_short_8: N3DOP3WM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N3DOP3WMQ4AVB57DNG4R5HVV7I \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6ec6e7eecc870150f7e369b91e9eb5fa3ba983aa26607206f4ec64f52809eb77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5921bd9acc6104c6872fa70042fbbe0697722fa9a86629f07c08c6088b77e213",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-12T03:33:10Z",
    "title_canon_sha256": "8ad1076e662d194d90ac3e5b84853f83bc90326ef40857885d3627ec4408df4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03129",
    "kind": "arxiv",
    "version": 1
  }
}